Simple Interest
Math MCQs

Question :    How much loan did Carol borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8812.5 to clear it?

Correct Answer  $7050

Solution & Explanation

Solution

Given,

Amount (A) = $8812.5

Rate of Simple Interest (R) = 5%

Time (T) = 5 years

Thus, Principal (P) = ?

Method (1) Using Formula

Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given

Formula to find the Principal (P)

Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)

⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]

⇒ A = P (1 + RT)

Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given

In the given question, we need to find the Principal (P)

Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get

$8812.5 = P (1 + 5% × 5)

⇒ $8812.5 = P (1 + ⁵/₁₀₀ × 5)

⇒ $8812.5 = P (1 + ^{5 × 5}/₁₀₀)

⇒ $8812.5 = P (1 + ²⁵/₁₀₀)

⇒ $8812.5 = P (^{100 + 25}/₁₀₀)

⇒ $8812.5 = P × ¹²⁵/₁₀₀

⇒ P × ¹²⁵/₁₀₀ = $8812.5

⇒ P = ^8812.5/_¹²⁵/100

⇒ P = 8812.5 × ¹⁰⁰/₁₂₅

⇒ P = ^{8812.5 × 100}/₁₂₅

⇒ P = ⁸⁸¹²⁵⁰/₁₂₅

⇒ P = $7050

Thus, the sum borrowed (P) = $7050 Answer

Method (1) Using Unitary Method

Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given

Calculation of the Simple Interest

Let, the principal = 100

Here, since rate of simple interest = 5% per annum

Thus, Interest = 5% of principal

⇒ Interest = 5% of 100 = 5

Thus, Simple Interest for 1 year = 5

Calculation of the Amount

Since, in the question, time = 5 years

So, we need to calculate the simple interest for the given time period, which is 5 years

Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year

= 5 × 5 = 25

Thus, simple interest for 5 years = 25

Thus, Amount (A) = Principal + Interest

⇒ Amount = 100 + 25 = 125

Calculation of the Principal

Now,

∵ If the Amount is 125, then the Principal = 100

∴ If the Amount is 1, then the Principal = ¹⁰⁰/₁₂₅

∴ If the Amount is 8812.5, then the Principal = ¹⁰⁰/₁₂₅ × 8812.5

= ^{100 × 8812.5}/₁₂₅

= ⁸⁸¹²⁵⁰/₁₂₅

= 7050

Thus, Principal = $7050

Thus, the sum borrowed = $7050 Answer

Similar Questions

(1) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.

(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?

(3) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.

(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?

(5) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.

(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.

(7) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.

(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.

(9) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 4 years.

(10) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.